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Unformatted text preview: Home > My Assignments > Section 8.9 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Friday, December 2, 2005 11:03 PM EST Description Applications of Taylor Current Score: 0 out of 12 Polynomials Question Score 1. [SCalcCC2 8.9.08.] Find the Taylor polynomial Tn(x) for the function f at the number a. Graph f and Tn on the same screen. pts subs 1 -/3 -/20 Notes T2(x) = (No Response) [2 + (1/2)*(x-1) + (3/16)*(x-1)^2] 2. [SCalcCC2 8.9.12.] You are given the following. pts subs 1 -/2 -/20 2 -/2 -/20 Notes f(x) = x-2, a = 1, n = 2, 0.9 x 1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a. T2(x) = (No Response) [1 - 2*(x-1) + 3*(x-1)^2] (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) Tn(x) when x lies in the given interval. (No Response)[0.00677] pts subs 1 -/1 -/20 Notes pts subs 1 -/2 -/20 2 -/2 -/20 Notes 3. [SCalcCC2 8.9.20.] How many terms of the Maclaurin series for ln(1 + x) do you need to use to estimate ln 1.4 to within 0.001? (No Response)[5] non-zero terms 4. [SCalcCC2 8.9.26.] The resistivity of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters ( m). The resistivity of a given metal depends on the temperature according to the equation below where t is the temperature in C. (t) = 20 e (t-20) There are tables that list the values of (called the temperature coefficient) and 20 (the resistivity at 20C) for various metals. Except at very low temperatures, the resistivity varies almost linearly with temperature and so it is common to approximate the expression for (t) by its first or second degree Taylor polynomial at t = 20. (a) Find expression for these linear and quadratic approximation. (Do this on paper. Your teacher may ask you to turn in this work.) (b) For copper, the tables give = 0.0039/C and 20 = 1.7 10-8 m. Graph the resistivity of copper and the linear and quadratic approximations for -250C t 1000C. (c) For what values of t does the linear approximation agree with the exponential expression to within one percent? (No Response)[-14]C t (No Response)[58]C Home My Assignments SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Home > My Assignments > Section 8.8 (Homework) About this Assignment Due: Friday, December 2, 2005 11:02 PM EST Description The Binomial Series Current Score: 11.5 out of 14.5 Question Score pts 1 1/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 8 0.25/0.25 9 0.25/0.25 10 0.25/0.25 11 0.25/0.25 12 0.25/0.25 13 0.25/0.25 4/4 subs 2/20 2/20 3/20 4/20 3/20 9/20 3/20 6/20 17/20 4/20 12/20 3/20 4/20 1. [SCalcCC2 8.8.04.] Use the binomial series to expand the function as a power series. State the radius of convergence. R=1 [1] Give the series using the form below. Viewing: Last Response View: All Responses Notes A=1 B=2 C=3 D=2 E = -1 F=2 G=5 H=8 I=3 J = -4 K=2 L=3 [1] [2] [3] [2] [-1] [2] [5] [8] [3] [-4] [2] [3] pts 1 1/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 8 0.25/0.25 9 0.25/0.25 10 0.25/0.25 11 0.25/0.25 12 0.25/0.25 13 0.25/0.25 14 0.25/0.25 15 0.25/0.25 4.5/4.5 subs 3/20 3/20 3/20 2/20 7/20 2/20 4/20 6/20 3/20 7/20 3/20 3/20 2/20 3/20 3/20 2. [SCalcCC2 8.8.06.] Use the binomial series to expand the function as a power series. State the radius of convergence. R=2 [2] Give the series using the form below. A=2 B=2 C=1 [2] [2] [1] Viewing: Last Response View: All Responses Notes D = -1 E=1 F=3 G=5 H=2 I = -1 J=2 K=2 L=1 M=2 N=2 [-1] [1] [3] [5] [2] [-1] [2] [2] [1] [2] [2] pts subs 1 3/3 2/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 0/3 1/20 0/3 Viewing: Last Response View: All Responses Notes 3. [SCalcCC2 8.8.12.] (a) Expand f(x) = (x + x2)/(1 - x)3 as a power series. (Do this on paper. Your teacher may ask you to turn in this work.) (b) Use part (a) to find the sum of the series below. 6 [6] 4. [SCalcCC2 8.8.14.] (a) Use the binomial series to find the Maclaurin series of the following. (Do this on paper. Your teacher may ask you to turn in this work.) (b) Use part (a) to evaluate f (9)(0). 0 [-113400] Home My Assignments ...
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This note was uploaded on 10/21/2009 for the course MATH MA241 taught by Professor Hubbard during the Spring '09 term at N.C. Central.

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